There is no real equivalent in the United States. November 11th, while recognised as Armistice Day, is officially known as Veterans Day and is a bank holiday, which this time will be on the Monday. I still haven't quite got used to the expression "Veterans", sometimes shortened to "Vets", which applies to all ex-servicemen, not just the very old ones and has nothing to do with animals.
(Incidentally, I've noticed that, in America, people who see a soldier in uniform will frequently go up and say, "Thank you for your service", even if they're complete strangers. I think that's rather touching. )
Veterans Day, November 11th, honours all former members of the armed services and not just those killed in action. So it doesn't have the poignancy of the British one. Memorial Day in May is more akin to our Remembrance Sunday but it has something cheerful and springlike about it and it's also considered the official beginning of the summer. There are parades and solemn ceremonies but not quite the sombre sadness of a November day of mourning.
Plus there is the poppy problem. Here they sell poppies for Memorial Day, not Veterans' day and while they're certainly well-meant, they're rather a poor shadow of the British ones, being poppy buds, rather than flowers, not very red and not very noticeable. You don't fix them with a pin but wind them round a button. And it's hard to find them. They don't sell them everywhere by any means. And I doubt that many people know what they're for. Still, we've saved a couple to wear on Sunday.
On my first Remembrance Sunday in America, I had managed to hang on to a British poppy, so I wore it and hubby a Canadian one he'd got over the border in Toronto, which was a rich, deep red and made of some velvetty stuff - classy but a little stiff. A girl who saw us remarked, "How romantic! You and your husband are both wearing red flowers!"